Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20265880 | C2 | semidirect |
| 2. #20265504 | C2 | semidirect |
| 3. #20265492 | C2 | semidirect |
| 4. #20265474 | C2 | semidirect |
| 5. #20265431 | C2 | semidirect |
| 6. C4×D808 | C2 | semidirect |
| 7. #20265256 | C2 | semidirect |
| 8. #20265216 | C2 | semidirect |
| 9. #499×C101 | C2 | semidirect |
| 103. C101 | #3355 | semidirect |
| 105. #499 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265880 | 2 |
| #20265504 | 2 |
| #20265492 | 2 |
| #20265474 | 2 |
| #20265431 | 2 |
| C4×D808 | 2 |
| #20265256 | 2 |
| #20265216 | 2 |
| #499×C101 | 2 |
| #3355 | 101 |